Question

example 1 reflect figures on the coordinate plane
the graph of △abc is shown.
graph the image of △abc after a reflection across the x - axis.
write the coordinates of the image.
part a graph the image of △abc after the reflection.
the x - axis is the line of reflection.
plot each vertex of △abc the same
distance from the x - axis as its corresponding
vertex on △abc.
point a is 2 units above the x - axis.
so, point a is plotted 2 units below the
x - axis.
point b is 3 units above the x - axis.
so, point b is plotted 3 units below the x - axis.
point c is 1 unit above the x - axis.
so, point c is plotted 1 unit below the x - axis.
part b write the coordinates of the image.
use the graph to write the coordinates of the vertices of the image.
a(5, 2) → a ( , )
b(1, 3) → b ( , )
c(-1, 1) → c ( , )

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) across the \(x\) - axis is \((x,y)\to(x, - y)\).

Step2: Find \(A'\) coordinates

For point \(A(5,2)\), using the reflection rule, the \(x\) - coordinate remains \(5\) and the \(y\) - coordinate becomes \(- 2\). So \(A'(5,-2)\).

Step3: Find \(B'\) coordinates

For point \(B(1,3)\), using the reflection rule, the \(x\) - coordinate remains \(1\) and the \(y\) - coordinate becomes \(-3\). So \(B'(1, - 3)\).

Step4: Find \(C'\) coordinates

For point \(C(-1,1)\), using the reflection rule, the \(x\) - coordinate remains \(-1\) and the \(y\) - coordinate becomes \(-1\). So \(C'(-1,-1)\).

Answer:

\(A'(5, - 2)\), \(B'(1, - 3)\), \(C'(-1, - 1)\)